What, if anything is wrong with the following reasoning? All horses are the same color. The proof is by induction on the number of horses. The base of the induction is easy: If there is one horse, then it is trivially the same color as itself. Now suppose that there are n horses, numbered 1 through n. By the induction hypothesis, horses 1 through n−1 have the sam e color (let’s say black). In particular, horse 2 is black. Also by the induction hypothesis, horses 2 through n have the same color. Since horse 2 is black, this means that horses 2 through n m ust be black. Therefore, all of the horses have the same color.
What, if anything is wrong with the following reasoning? All horses are the same color. The proof is by induction on the number of horses. The base of the induction is easy: If there is one horse, then it is trivially the same color as itself. Now suppose that there are n horses, numbered 1 through n. By the induction hypothesis, horses 1 through n−1 have the sam e color (let’s say black). In particular, horse 2 is black. Also by the induction hypothesis, horses 2 through n have the same color. Since horse 2 is black, this means that horses 2 through n m ust be black. Therefore, all of the horses have the same color.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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What, if anything is wrong with the following reasoning? All horses are the same color. The proof is by induction on the number of horses. The base of the induction is easy: If there is one horse, then it is trivially the same color as itself. Now suppose that there are n horses, numbered 1 through n. By the induction hypothesis, horses 1 through n−1 have the sam e color (let’s say black). In particular, horse 2 is black. Also by the induction hypothesis, horses 2 through n have the same color. Since horse 2 is black, this means that horses 2 through n m ust be black. Therefore, all of the horses have the same color.
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